arXiv subjects

George Dasoulas

Publications and source records attributed to George Dasoulas.

24 records · Page 2Linked to original sources

arXiv2021

Lipschitz Normalization for Self-Attention Layers with Application to Graph Neural Networks

Attention based neural networks are state of the art in a large range of applications. However, their performance tends to degrade when the number of layers increases. In this work, we show that enforcing Lipschitz continuity by normalizing the attention scores can significantly improve the performance of deep attention models. First, we show that, for deep graph attention networks (GAT), gradient explosion appears during training, leading to poor performance of gradient-based training algorithms. To address this issue, we derive a theoretical analysis of the Lipschitz continuity of attention modules and introduce LipschitzNorm, a simple and parameter-free normalization for self-attention mechanisms that enforces the model to be Lipschitz continuous. We then apply LipschitzNorm to GAT and Graph Transformers and show that their performance is substantially improved in the deep setting (10 to 30 layers). More specifically, we show that a deep GAT model with LipschitzNorm achieves state of the art results for node label prediction tasks that exhibit long-range dependencies, while showing consistent improvements over their unnormalized counterparts in benchmark node classification tasks.

cs.LG↗

arXiv2021

Graph-based Neural Architecture Search with Operation Embeddings

Neural Architecture Search (NAS) has recently gained increased attention, as a class of approaches that automatically searches in an input space of network architectures. A crucial part of the NAS pipeline is the encoding of the architecture that consists of the applied computational blocks, namely the operations and the links between them. Most of the existing approaches either fail to capture the structural properties of the architectures or use hand-engineered vector to encode the operator information. In this paper, we propose the replacement of fixed operator encoding with learnable representations in the optimization process. This approach, which effectively captures the relations of different operations, leads to smoother and more accurate representations of the architectures and consequently to improved performance of the end task. Our extensive evaluation in ENAS benchmark demonstrates the effectiveness of the proposed operation embeddings to the generation of highly accurate models, achieving state-of-the-art performance. Finally, our method produces top-performing architectures that share similar operation and graph patterns, highlighting a strong correlation between the structural properties of the architecture and its performance.

cs.LG↗

arXiv2021

Ego-based Entropy Measures for Structural Representations on Graphs

Machine learning on graph-structured data has attracted high research interest due to the emergence of Graph Neural Networks (GNNs). Most of the proposed GNNs are based on the node homophily, i.e neighboring nodes share similar characteristics. However, in many complex networks, nodes that lie to distant parts of the graph share structurally equivalent characteristics and exhibit similar roles (e.g chemical properties of distant atoms in a molecule, type of social network users). A growing literature proposed representations that identify structurally equivalent nodes. However, most of the existing methods require high time and space complexity. In this paper, we propose VNEstruct, a simple approach, based on entropy measures of the neighborhood's topology, for generating low-dimensional structural representations, that is time-efficient and robust to graph perturbations. Empirically, we observe that VNEstruct exhibits robustness on structural role identification tasks. Moreover, VNEstruct can achieve state-of-the-art performance on graph classification, without incorporating the graph structure information in the optimization, in contrast to GNN competitors.

cs.LG↗

arXiv2020

k-hop Graph Neural Networks

Graph neural networks (GNNs) have emerged recently as a powerful architecture for learning node and graph representations. Standard GNNs have the same expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of distinguishing non-isomorphic graphs. However, it was recently shown that this test cannot identify fundamental graph properties such as connectivity and triangle freeness. We show that GNNs also suffer from the same limitation. To address this limitation, we propose a more expressive architecture, k-hop GNNs, which updates a node's representation by aggregating information not only from its direct neighbors, but from its k-hop neighborhood. We show that the proposed architecture can identify fundamental graph properties. We evaluate the proposed architecture on standard node classification and graph classification datasets. Our experimental evaluation confirms our theoretical findings since the proposed model achieves performance better or comparable to standard GNNs and to state-of-the-art algorithms.

stat.ML↗

arXiv2020

Ego-based Entropy Measures for Structural Representations

In complex networks, nodes that share similar structural characteristics often exhibit similar roles (e.g type of users in a social network or the hierarchical position of employees in a company). In order to leverage this relationship, a growing literature proposed latent representations that identify structurally equivalent nodes. However, most of the existing methods require high time and space complexity. In this paper, we propose VNEstruct, a simple approach for generating low-dimensional structural node embeddings, that is both time efficient and robust to perturbations of the graph structure. The proposed approach focuses on the local neighborhood of each node and employs the Von Neumann entropy, an information-theoretic tool, to extract features that capture the neighborhood's topology. Moreover, on graph classification tasks, we suggest the utilization of the generated structural embeddings for the transformation of an attributed graph structure into a set of augmented node attributes. Empirically, we observe that the proposed approach exhibits robustness on structural role identification tasks and state-of-the-art performance on graph classification tasks, while maintaining very high computational speed.

cs.LG↗

arXiv2019

Coloring graph neural networks for node disambiguation

In this paper, we show that a simple coloring scheme can improve, both theoretically and empirically, the expressive power of Message Passing Neural Networks(MPNNs). More specifically, we introduce a graph neural network called Colored Local Iterative Procedure (CLIP) that uses colors to disambiguate identical node attributes, and show that this representation is a universal approximator of continuous functions on graphs with node attributes. Our method relies on separability , a key topological characteristic that allows to extend well-chosen neural networks into universal representations. Finally, we show experimentally that CLIP is capable of capturing structural characteristics that traditional MPNNs fail to distinguish,while being state-of-the-art on benchmark graph classification datasets.

cs.LG↗